The newly enthroned Archbishop of Canterbury has offered to hold an in-person meeting with a gay rights activist after criticism over the Church of England's opposition to same-sex marriage.

The Rev. Justin Welby, who was enthroned as leader of the Church of England on Thursday, sent a message to UK-based activist Peter Tatchell the day before responding to an open letter by the rights campaigner.

"Thank you for your very thoughtful letter. It requires much thought and the points it makes are powerful. I would like to explain what I think to you...and listen to you in return," Welby was quoted as saying by the UK-based New Statesman magazine.

In an interview with the BBC ahead of his enthronement, Welby said, "You see gay relationships that are just stunning in the quality of the relationship."

The Archbsihop said he stood by the church's position in opposition to same-sex marriage but added he was "challenged as to how we respond to it."

"The Church of England holds very firmly, and continues to hold to the view, that marriage is a lifelong union of one man to one woman," he said in the interview.

"At the same time, at the heart of our understanding of what it is to be human, is the essential dignity of the human being. And so we have to be very clear about homophobia," he added.

In an open letter, Tatchell accused Welby of being "homophobic."

"You claim that you are not homophobic but a person who opposes legal equality for LGBT people is homophobic – in the same way that a person who opposes equal rights for black people is racist," Tachell said in a letter published on the website of the New Statesman.

Tatchell argued in the letter that "discrimination is not a Christian value; regardless of whether this discrimination concerns gender, race, faith, sexual orientation or gender identity."

He called on Welby to speak out against proposed laws in Uganda and Nigeria that further criminalize homosexuality.

"I urge you to speak out against these totalitarian homophobic proposals," Tatchell said.

The gay-rights campaigner said he has spoken out against the prosecution of street preachers and persecuted Christians in Saudi Arabia and Pakistan and called on Welby to "reciprocate."

"Would you make such compromises on equal rights in the case of ethnic minorities? I expect not. So why should LGBT people be treated differently?"